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In the shadows of a hypergraph: looking for associated primes of powers of square-free monomial ideals

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1 Published in 2019 at "Journal of Algebraic Combinatorics"

DOI: 10.1007/s10801-019-00915-5

Abstract: The aim of this paper is to study the associated primes of powers of square-free monomial ideals. Each square-free monomial ideal corresponds uniquely to a finite simple hypergraph via the cover ideal construction, and vice… read more here.

Keywords: free monomial; hypergraph; associated primes; square free ... See more keywords

On Monomial Ideals and Their Socles

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1 Published in 2020 at "Order"

DOI: 10.1007/s11083-019-09509-z

Abstract: For a finite subset M ⊂ [ x 1 ,…, x d ] of monomials, we describe how to constructively obtain a monomial ideal I ⊆ R = K [ x 1 , … ,… read more here.

Keywords: ideals socles; monomial ideals;

Membership Criteria and Containments of Powers of Monomial Ideals

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0 Published in 2019 at "Acta Mathematica Vietnamica"

DOI: 10.1007/s40306-018-00325-y

Abstract: We present a close relationship between matching number, covering numbers and their fractional versions in combinatorial optimization and ordinary powers, integral closures of powers, and symbolic powers of monomial ideals. This relationship leads to several… read more here.

Keywords: containments powers; criteria containments; powers monomial; membership criteria ... See more keywords

Integral closure and bounds for quotients of multiplicities of monomial ideals

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1 Published in 2018 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2017.12.030

Abstract: Abstract Given a pair of monomial ideals I and J of finite colength of the ring of analytic function germs ( C n , 0 ) → C , we prove that some power of… read more here.

Keywords: quotients multiplicities; integral closure; bounds quotients; closure bounds ... See more keywords

Pruned cellular free resolutions of monomial ideals

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0 Published in 2020 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2019.09.013

Abstract: Using discrete Morse theory, we give an algorithm that prunes the excess of information in the Taylor resolution and constructs a new cellular free resolution for an arbitrary monomial ideal. The pruned resolution is not… read more here.

Keywords: resolution; pruned cellular; cellular free; resolutions monomial ... See more keywords

Monomial ideals with arbitrarily high tiny powers in any number of variables

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0 Published in 2019 at "Communications in Algebra"

DOI: 10.1080/00927872.2020.1772276

Abstract: Abstract Powers of (monomial) ideals is a subject that still calls attraction in various ways. Let be a monomial ideal and let G(I) denote the (unique) minimal monomial generating set of I. How small can… read more here.

Keywords: tiny powers; high tiny; ideals arbitrarily; powers number ... See more keywords

The saturation number of monomial ideals

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1 Published in 2022 at "Communications in Algebra"

DOI: 10.1080/00927872.2023.2178658

Abstract: Abstract Let be the polynomial ring over a field and be the homogeneous maximal ideal of S. For an ideal , let be the minimum number k for which . In this paper, we compute… read more here.

Keywords: number monomial; saturation number; monomial ideals; number ... See more keywords

Monomial Ideals with Quasi-Linear Quotients

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0 Published in 2019 at "Lobachevskii Journal of Mathematics"

DOI: 10.1134/s1995080219010116

Abstract: In this paper, we extend the notion of quasi-linear quotients for a pure monomial ideal (not necessarily square-free) of degree d. We introduce the notion of quasi-linear free resolution and show that if a pure… read more here.

Keywords: admits quasi; pure monomial; linear quotients; monomial ideals ... See more keywords

Persistence property for some classes of monomial ideals of a polynomial ring

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0 Published in 2017 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498817501055

Abstract: Let K be a field and R = K[x1,…,xn] be a polynomial ring in the variables x1,…,xn. In this paper, we introduce two classes of monomial ideals of R, which have the following properties: (i)The… read more here.

Keywords: classes monomial; persistence property; polynomial ring; property classes ... See more keywords